Global geometry optimization of silicon clusters described by three empirical potentials

Abstract

The “basic-hopping” global optimization technique developed by Wales and Doye is employed to study the global minima of silicon clusters Si n (3⩽n⩽30) with three empirical potentials: the Stillinger–Weber (SW), the modified Stillinger–Weber (MSW), and the Gong potentials. For the small-sized SW and Gong clusters (3⩽n⩽15), it is found that the global minima obtained based on the basin-hopping method are identical to those reported by using the genetic algorithm [Iwamatsu, J. Chem. Phys. 112, 10976 (2000)], as well as with those by using molecular dynamics and the steepest-descent quench (SDQ) method [Feuston, Kalia, and Vashishta, Phys. Rev. B 37, 6297 (1988)]. However, for the mid-sized SW clusters (16⩽n⩽20), the global minima obtained differ from those based on the SDQ method, e.g., the appearance of the endohedral atom with fivefold coordination starting at n=17, as opposed to n=19. For larger SW clusters (20⩽n⩽30), it is found that the “bulklike” endohedral atom with tetrahedral coordination starts at n=20. In particular, the overall structural features of SW Si 21 , Si 23 , Si 25 , and Si 28 are nearly identical to the MSW counterparts. With the SW Si 21 as the starting structure, a geometric optimization at the B3LYP/6-31G(d) level of density-functional theory yields an isomer similar to the ground-state- isomer of Si 21 reported by Pederson et al. [Phys. Rev. B 54, 2863 (1996)].